Class 12 Physics · Original EZT practice
Electrostatic Potential and Capacitance (Class 12 Chapter 2): summary and practice
Electrostatic Potential and Capacitance moves from forces to energy: the potential V = kq/r (a scalar), equipotential surfaces, potential energy of charge systems, conductors and dielectrics, the parallel plate capacitor C = eps0 A/d, series and parallel combinations, and the stored energy U = (1/2) C V^2. All questions are original EZT tutor practice following the chapter's own section order.
6 original worked examples, 6 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 21 October 2026:
1. Electrostatic potential
Potential is potential energy per unit charge: the work done bringing a unit positive charge from infinity to a point. For a point charge, V = kq/r - a scalar, so potentials from many charges simply add.
2. Equipotential surfaces
An equipotential surface has the same potential everywhere, so no work is done moving a charge along it. Field lines always cross equipotential surfaces at right angles, and the field points from higher to lower potential.
3. Conductors and dielectrics
Inside a conductor in electrostatic equilibrium the field is zero and the whole body is one equipotential; a cavity inside is shielded from outside fields. Dielectrics polarise instead - their molecules align against the applied field and weaken it by the factor K.
4. Capacitors and stored energy
A parallel plate capacitor holds C = eps0 A/d, and a dielectric multiplies that by K. Capacitors combine opposite to resistors: series adds reciprocals, parallel adds directly. The stored energy is U = (1/2) C V^2.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Potential near a point charge
Choose the method: V = kq/r with k = 9 x 10^9 - add scalars, no directions.
EZT practice question
Potential at 0.1 m from a 1 microcoulomb charge?
Show the worked solution
- V = kq/r.
- = 9 x 10^9 x 10^-6 / 0.1.
- = 9.0 x 10^4.
Answer: V = 9.0 x 10^4 volts.
Check: Halving the distance doubles V - at 0.05 m the same charge gives 1.8 x 10^5 V, the inverse-r pattern.
Watch for this: Potential is a SCALAR - do not split it into components like a field.
Now try it yourself
V at 0.2 m from 2 microcoulombs?
Check your answer
9.0 x 10^4 V.
9 x 10^9 x 2 x 10^-6 / 0.2 - double charge, double distance.
Potential energy of two charges
Choose the method: U = k q1 q2 / r - sign included.
EZT practice question
Potential energy of 1 microcoulomb and 2 microcoulombs held 0.5 m apart?
Show the worked solution
- U = k q1 q2 / r.
- = 9 x 10^9 x 10^-6 x 2 x 10^-6 / 0.5.
- = 18 x 10^-3 / 0.5.
Answer: U = 0.036 J.
Check: Both charges are positive, so U > 0 - work really was needed to push them together, which matches.
Watch for this: Keep the SIGNS of q1 and q2 - opposite signs give negative U, meaning attraction.
Now try it yourself
U for 1 and -2 microcoulombs 0.5 m apart?
Check your answer
-0.036 J.
Same magnitude, opposite sign - the pair attracts.
Capacitance of a parallel plate capacitor
Choose the method: C = eps0 A / d, eps0 = 8.85 x 10^-12.
EZT practice question
Capacitance of plates with A = 0.01 m^2 separated by d = 1 mm?
Show the worked solution
- C = eps0 A / d.
- = 8.85 x 10^-12 x 0.01 / 10^-3.
- = 8.85 x 10^-11.
Answer: C = 8.85 x 10^-11 F, about 88.5 picofarads.
Check: Real capacitors of this size are indeed picofarads - the farad is a huge unit, so a tiny answer is expected.
Watch for this: Convert millimetres to metres FIRST: d = 1 mm = 10^-3 m, not 1.
Now try it yourself
Same plates at d = 0.5 mm?
Check your answer
1.77 x 10^-10 F.
Halving d doubles C.
Effect of a dielectric
Choose the method: A dielectric multiplies capacitance by its constant K.
EZT practice question
The 88.5 pF capacitor is filled with a dielectric of K = 4. New capacitance?
Show the worked solution
- Dielectric polarisation opposes the field.
- C becomes K times the vacuum value.
- C = 4 x 88.5 pF.
Answer: C = 354 pF.
Check: At fixed charge the voltage drops by the same factor K - the capacitor stores more charge at the same voltage, which is the whole point.
Watch for this: The dielectric RAISES capacitance - forgetting that flips every calculation after it.
Now try it yourself
K = 2 fills half the gap (in series with air). Intuition check: does C rise?
Check your answer
Yes, though less than doubling.
Any dielectric insertion weakens the field somewhere, so C always increases.
Series and parallel combinations
Choose the method: Series: 1/C = 1/C1 + 1/C2. Parallel: C = C1 + C2.
EZT practice question
Combine 2 microfarad and 3 microfarad capacitors (a) in series (b) in parallel.
Show the worked solution
- Series: 1/C = 1/2 + 1/3 = 5/6.
- C = 6/5 = 1.2.
- Parallel: C = 2 + 3.
Answer: Series 1.2 microfarad, parallel 5 microfarad.
Check: Series gives less than the smallest capacitor (1.2 < 2) and parallel gives the sum - the sane-bounds test passes.
Watch for this: Capacitors combine OPPOSITE to resistors - series adds reciprocals here.
Now try it yourself
Two 4 microfarad capacitors in series?
Check your answer
2 microfarad.
1/C = 1/4 + 1/4 = 1/2.
Energy stored in a capacitor
Choose the method: U = (1/2) C V^2 - also (1/2) QV or Q^2/2C.
EZT practice question
Energy stored when the 88.5 pF capacitor is charged to 100 V?
Show the worked solution
- U = (1/2) C V^2.
- = 0.5 x 8.85 x 10^-11 x 10^4.
- = 4.4 x 10^-7.
Answer: U = 4.4 x 10^-7 J, about 0.44 microjoules.
Check: Doubling the voltage quadruples the energy - the V-squared dependence is the check to run.
Watch for this: The factor 1/2 is real - it comes from the average voltage during charging, which rises from zero.
Now try it yourself
Same capacitor at 200 V?
Check your answer
1.77 x 10^-6 J.
Four times the 100 V energy.
Try a mixed set
Choose a method or explanation before opening each answer.
1. V of a point charge?
Show answer and reason
V = kq/r, a scalar.
Scalars add directly for many charges.
2. Field inside a conductor?
Show answer and reason
Zero in equilibrium.
Free charges rearrange until it vanishes.
3. Parallel plate C?
Show answer and reason
C = eps0 A/d, times K with dielectric.
Bigger plates and thinner gaps store more.
4. Stored energy?
Show answer and reason
U = (1/2) C V^2.
Charging works against a rising voltage.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Find V at 0.2 m from a 2 microcoulomb charge.
- Two 4 microfarad capacitors in series - equivalent C?
- Energy stored in an 88.5 pF capacitor at 100 V.
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Questions about this practice page
- What is the difference between potential and potential energy?
- Potential is per unit charge - a property of the point in the field, measured in volts. Potential energy belongs to a specific charge placed there: U = qV. One describes the field, the other the charge-field pair.
- Why does a dielectric increase capacitance?
- The dielectric's molecules polarise and set up an internal field opposing the applied one, so the net field (and voltage) drops for the same stored charge. Since C = Q/V, a smaller V for the same Q means a larger C, by the factor K.
- Why do capacitors combine opposite to resistors?
- In series the same charge sits on each capacitor and voltages add, so the reciprocals add. In parallel the voltage is shared and charges add, so capacitances add - the mirror image of the resistor rules.
- Why is the field inside a conductor zero but the potential constant?
- Free electrons move until no field remains to push them - that is equilibrium. With E = 0 everywhere inside, no work moves a charge within the conductor, so every point sits at the same potential.
- Are these the NCERT exercise questions for Electrostatic Potential and Capacitance (Class 12)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.